c please! hint below EQUATIONS OF THE FIRST DEGREE 7.8 the problem of finding al

Question

c please! hint below

EQUATIONS OF THE FIRST DEGREE 7.8 the problem of finding all integral so tions of The Hindus solved egers linear equation ax t by c. where a, b c are inte (a) f ax an integral solution, show that th is common divisor of a and b is a theorem says that in generality if we consider a and b to be relatively prime a and b if and ntegral solution are given are relatively prime, show that all integral solutions mb, y y, ma, where m is an arbitrary integer IThis theoret says that all integral solutions are known if just 1 integral s can be found. A simple way of finding 1 integral solution is illustrated in the or Problem Study c c) olve 7x 16y 209 for positive integral solutions Solve 23x 37y 3000 for positive integral solutions.

Explanation / Answer

c) 7x + 16y = 209

Let y = 3

Then 7x + 48 = 209

7x = 161

x = 23

Now to find other solution, add coefficent of x into value of y:

another solution, y = 3 + 7 = 10

Then x = 7

So, two positive solutions are there.

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